I am staying at a hotel on Soi 18 and its pretty close to Asoke and Sukhumvit stations. I arrive on a Saturday night around 9 PM and leave the next sunday morning around 8:30 AM for the airport. What is traffic like on the weekends? Does the train run less often on the weekends?

Traffic, if considering a taxi, should not impact your journey given the days of week, time of day.

While there is an overhead enclosed walkway in/around Asoke interconnecting the Skytrain (BTS) and Subway (MRT) you may still have an unsheltered walk near/down Soi 18. It is rainy season now so remember to pack waders and an umbrella if you plan to walk from the MRT/BTS.